Fig. 1: Pseudo spin guiding in NLPC.

a Electron spin waveguide via magnetic domain walls with sharp edges. In the spin picture, an electron (1/2 spinor with arbitrary direction, pink) enters a magnetized material where the material magnetization abruptly changes from spin up (blue arrows) to spin down (purple arrows) perpendicular to the propagation direction (black arrow). This magnetization texture induces a spin-dependent potential that guides spin-up electrons and scatters spin-down electrons. b Guiding PS light beams in NLPCs. In the optical picture, narrow (in the ‘x’ direction) periodically poled NLPC is analogous to the behavior of magnetic domain walls with sharp edges. The combined effect of a wide and powerful pump beam (yellow) with the fabricated ferroelectric domain walls induces the analog magnetization for the frequency superposition states and acts as a PS waveguide core and cladding. This allows the guiding of a frequency superposition state with a specific relative phase between the idler (red) and signal (green) fields while allowing regular diffraction in the ‘y’ direction. c Microscopic top images after selective etching of the fabricated NLPC. Red specifies the designed pattern. Note that due to the KTP anisotropy^23,24, the structure is not ideal and shows spikes in the reversed ferroelectricity, but it is still sufficient to confine the light beams (See supplementary materials). d Simulation of the signal and idler propagation inside the NLPC. ‘X’–‘Z’ cross section. An idler input frequency is a superposition of \({\psi }_{+}\) and \({\psi }_{-}\). One of the eigenstates (\({\psi }_{+}\)) is fully guided inside the PS waveguide structure. Next to it is the diffracted, scattered eigenstate (\({\psi }_{-}\)).